1. Solve analytically ( 1 pt.): $$ y^{\prime}=y x^{2}-y \text { with } y(0)=1 $$ 2. Use a numerical method to solve the same differential equation (show your program code) (5 pts.) 3. Plot the analytical solution and compare it with the numerical answer with 3 different step lengths. The plot has to be in the $x=(-3,2.5)$ inteval ( 2 pts.) 4. Plot the analytical solution and compare it with the numerical answer of the Euler and improbed Euler methods with the same step lengths. The plot has to be in the $x=(-3,2.5)$ inteval ( 2 pts.) CS.JG.065